A multinomial extension of an inequality of Haber.
A new class of symmetric functions.
A new estimate for the vertex number of an edge-regular graph.
A `nice' bijection for a content formula for skew semistandard Young tableaux.
A normalization formula for the Jack polynomials in superspace and an identity on partitions.
A note on another construction of graphs with vertices and cyclic automorphism group of order
The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having vertices and automorphism group cyclic of order , . As a special case we get graphs with vertices and cyclic automorphism groups of order . It can revive interest in related problems.
A note on exponents vs root heights for complex simple Lie algebras.
A note on Jeu de Taquin
A direct formula for jeu de taquin applied to the swap of two rows of standard tableaux is given. A generalization of this formula to non standard tableaux is used to describe combinatorially a path basis isomorphism for the algebra of type .
A note on symmetric powers of the standard representation of .
A note on three types of quasisymmetric functions.
A -analogue of a formula of Frobenius.
A Pfaffian-Hafnian analogue of Borchardt's identity.
A Pieri-type formula for even orthogonal Grassmannians
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
A plethysm formula for .
A positive proof of the Littlewood-Richardson rule using the octahedron recurrence.
A prolific construction of strongly regular graphs with the -e. c. property.
A proof of the identities of Gordon and MacMahon and two new identities. (La démonstration des identités de Gordon et MacMahon et de deux identités nouvelles.)
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...
A quasi-spectral characterization of strongly distance-regular graphs.